Finite Group Databasebeta

← #33112027

Subgroups — #33112027

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14556559C211yesmaximal, characteristic
2#22610727C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610543C211yesmaximal, characteristic, complemented
5#22610541C211yesmaximal, characteristic, complemented
6#22610537C211yesmaximal, characteristic, complemented
7#22610537C211yesmaximal, characteristic, complemented
8#22610536C211yesmaximal, characteristic, complemented
9#22610534C211yesmaximal, characteristic, complemented
10#22610229C211yesmaximal, characteristic, complemented
11#22610226C211yesmaximal, characteristic, complemented
12#22610226C211yesmaximal, characteristic, complemented
13#22609840C211yesmaximal, characteristic, complemented
14#22609840C211yesmaximal, characteristic, complemented
15C73×#1954C211yesmaximal, characteristic, complemented
16C23×C4×D73C2211yescharacteristic
17C22×#11924012C2211yescharacteristic, complemented
18C2×#14556559C411yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×C4×C22⋊D73C2211yescharacteristic
21C2×#14556520C2211yescharacteristic, complemented
22C2×#14556520C2211yescharacteristic, complemented
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic, complemented
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556503C2211yescharacteristic
34C2×#14556501C2211yescharacteristic, complemented
35C2×C8×Dic73C2211yescharacteristic, complemented
36#17988467C411yescharacteristic
37#17988463C411yescharacteristic
38#17988463C411yescharacteristic
39#17988459C411yescharacteristic
40#17988458C411yescharacteristic
41#17988458C411yescharacteristic
42#17988442C411yescharacteristic
43C4×#11924005C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988342C2211yescharacteristic, complemented
47#17988342C2211yescharacteristic, complemented
48#17988341C2211yescharacteristic, complemented
49#17988341C2211yescharacteristic, complemented
50#17988341C2211yescharacteristic, complemented
51#17988341C2211yescharacteristic, complemented
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic, complemented
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic, complemented
57C2×C22⋊C8×C73C2211yescharacteristic, complemented
58C2×C4×C8×C73C2211yescharacteristic, complemented
59C24×D73C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C22⋊D73C2×C411yescharacteristic
62C23×Dic73C2×C411yescharacteristic
63C22×C4×D73—41no—
64C22×C4×D73—41no—
65C22×C4×D73—41no—
66C22×C4×D73—41no—
67C22×C4×D73—41no—
68C22×C4×D73—41no—
69C22×C4×D73C2×C411yescharacteristic
70C22×C4×D73C2×C411yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C2×#11924012—41no—
74C2×#11924012—41no—
75C2×#11924012—41no—
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80#14556559—24no—
81C4×C22⋊D73—41no—
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C4×C22⋊D73—41no—
85C2×#11924007C2×C411yescharacteristic
86C2×#11924007C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×C22⋊Dic73C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×#11924005C2×C411yescharacteristic
96C2×#11924005C2×C411yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98C2×C4×Dic73C2311yescharacteristic
99#14556520—41no—
100#14556520—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103C22⋊#10596831—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109#14556503—41no—
110#14556503—41no—
111#14556503—41no—
112#14556501—41no—
113C8×Dic73—41no—
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119#14556498C2×C411yescharacteristic
120C22×D4×C73C2×C411yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C23×C4×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C22×C8×C73C2311yescharacteristic
127C4×D4×C73—41no—
128C4×D4×C73—41no—
129C2×C4⋊C4×C73C2×C411yescharacteristic
130C2×C22⋊C4×C73C2×C411yescharacteristic
131C2×C22⋊C4×C73C2×C411yescharacteristic
132C2×C42×C73C2311yescharacteristic
133C4⋊C8×C73—41no—
134C22⋊C8×C73—41no—
135C22⋊C8×C73—41no—
136C22⋊C8×C73—41no—
137C22⋊C8×C73—41no—
138C4×C8×C73—41no—
139C23×D73—22no—
140C23×D73—22no—
141C23×D73—22no—
142C23×D73—41no—
143C23×D73—41no—
144C23×D73—41no—
145C23×D73—41no—
146C23×D73C22×C411yescharacteristic
147C23×D73C22×C411yescharacteristic
148C2×C22⋊D73—22no—
149C2×C22⋊D73—22no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73—41no—
152C2×C22⋊D73—41no—
153C2×C22⋊D73—41no—
154C22×Dic73—41no—
155C22×Dic73—41no—
156C22×Dic73—41no—
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C22×Dic73C22×C411yescharacteristic
162C22×Dic73C22×C411yescharacteristic
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—21no—
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—41no—
176C2×C4×D73—41no—
177C2×C4×D73—41no—
178C2×C4×D73—41no—
179C2×C4×D73—41no—
180C2×C4×D73—41no—
181C2×C4×D73—44no—
182C2×C4×D73—44no—
183C2×C4×D73—44no—
184C2×C4×D73—44no—
185#11924012—44no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831—21no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198#11924007—41no—
199#11924007—41no—
200C22⋊Dic73—22no—
201C22⋊Dic73—22no—
202C22⋊Dic73—41no—
203C22⋊Dic73—41no—
204#11924005—22no—
205#11924005—22no—
206#11924005—41no—
207#11924005—41no—
208#11924005—41no—
209#11924005M1614yescomplemented
210C4×Dic73—21no—
211C4×Dic73—21no—
212C4×Dic73—21no—
213C4×Dic73—21no—
214C24×C73C22×C411yescharacteristic
215C24×C73C22×C411yescharacteristic
216C2×D4×C73—22no—
217C2×D4×C73—22no—
218C2×D4×C73—41no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C2411yescharacteristic
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C4⋊C4×C73—41no—
249C22⋊C4×C73—41no—
250C22⋊C4×C73—41no—
251C42×C73—21no—
252C42×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73#13112yes—
267C23×C73C23×C411yescharacteristic
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73—21no—
279C22×D73—21no—
280C22×D73—44no—
281C22×D73—44no—
282C22×D73—44no—
283C22×D73—44no—
284C22×D73—44no—
285C22×D73—44no—
286C22×D73—44no—
287C22×D73C2×M1612yes—
288C22×D73#13112yes—
289D4×C73—44no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73C2×M1612yes—
310C2×C4×C73H(5,𝔽2)11yescharacteristic
311C2×C4×C73H(5,𝔽2)11yescharacteristic
312C2×C4×C73H(5,𝔽2)11yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C2×C4×C73H(5,𝔽2)11yescharacteristic
315C2×C4×C73H(5,𝔽2)11yescharacteristic
316C22⋊D73—44no—
317C22⋊D73—44no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73—21no—
326C2×Dic73—21no—
327C2×Dic73—21no—
328C2×Dic73—21no—
329C2×Dic73—21no—
330C2×Dic73—21no—
331C2×Dic73—21no—
332C2×Dic73—21no—
333C2×Dic73—21no—
334C2×Dic73—21no—
335C2×Dic73—44no—
336C2×Dic73C2×M1612yes—
337C4×D73—44no—
338C4×D73—44no—
339C4×D73—41no—
340C4×D73—41no—
341C4×D73—41no—
342C4×D73—41no—
343C4×D73—41no—
344C4×D73—41no—
345C4×D73—41no—
346C4×D73—41no—
347C8×C73—41no—
348C8×C73—41no—
349C8×C73—41no—
350C8×C73—41no—
351#10596831—41no—
352#10596831—41no—
353#10596831—41no—
354#10596831—41no—
355C22×C73—22no—
356C22×C73—22no—
357C22×C73—22no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73#51811yescharacteristic
370C22×C73#51811yescharacteristic
371C22×C73#51811yescharacteristic
372C22×C73C22×M1611yescharacteristic
373C22×C73C2×#13111yescharacteristic
374C22×C73C2×#13111yescharacteristic
375C22×C73#56811yescharacteristic
376C2×D73—22no—
377C2×D73—22no—
378C2×D73—22no—
379C2×D73—22no—
380C2×D73—22no—
381C2×D73—22no—
382C2×D73—416no—
383C2×D73—41no—
384C2×D73—41no—
385C2×D73—41no—
386C2×D73—41no—
387C2×D73—41no—
388C2×D73—41no—
389C2×D73—41no—
390C2×D73—41no—
391C4×C73—22no—
392C4×C73—41no—
393C4×C73—41no—
394C4×C73—41no—
395C4×C73#56011yescharacteristic
396C4×C73#56011yescharacteristic
397C4×C73#56011yescharacteristic
398C4×C73H(3,𝔽4)11yescharacteristic
399Dic73—22no—
400Dic73—41no—
401Dic73—41no—
402Dic73—41no—
403Dic73—41no—
404Dic73—41no—
405#23308—731nomaximal, Sylow
406C2×C73—42no—
407C2×C73—81no—
408C2×C73#237511yescharacteristic
409C2×C73#297411yescharacteristic
410C2×C73#297411yescharacteristic
411C2×C73#297511yescharacteristic
412C2×C73#297611yescharacteristic
413C2×C73#297611yescharacteristic
414C2×C73#297711yescharacteristic
415D73—42no—
416D73—42no—
417C4×#120—731no—
418#1955—731no—
419#1954—731no—
420#1954D7311yescharacteristic, complemented
421#1924—731no—
422#1924—731no—
423#1923—731no—
424#1923—731no—
425#1923—731no—
426#1923—731no—
427#1870—731no—
428#1870—731no—
429#1870—731no—
430#1779—731no—
431#1779—731no—
432C73#2330811yescharacteristic, complemented, Sylow
433C24×C4—731no—
434C22×M16—731no—
435C2×#120—731no—
436C2×C4×D4—731no—
437C2×C4×D4—731no—
438C2×C4×D4C2×D7311yescharacteristic
439C2×C4⋊C8—731no—
440C2×C4⋊C8—731no—
441C2×C4⋊C8C2×D7311yescharacteristic, complemented
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×C22⋊C8—731no—
452C2×C22⋊C8—731no—
453C2×C22⋊C8C2×D7311yescharacteristic
454C2×C22⋊C8C2×D7311yescharacteristic
455C2×C22⋊C8C2×D7311yescharacteristic, complemented
456C2×C22⋊C8C2×D7311yescharacteristic, complemented
457C2×#97—731no—
458C2×C4×C8—731no—
459C2×C4×C8C2×D7311yescharacteristic, complemented
460#386—731no—
461#386—731no—
462#386—731no—
463#385—731no—
464#385—731no—
465#385—731no—
466#379—731no—
467C4×C22⋊C4—731no—
468C4×C22⋊C4—731no—
469C4×C22⋊C4—731no—
470#336—731no—
471#336—731no—
472#336—731no—
473#336—731no—
474#336—731no—
475#336—731no—
476C25—731no—
477C22×D4—731no—
478C22×D4—731no—
479C22×D4C4×D7311yescharacteristic
480C23×C4—2921no—
481C23×C4—2921no—
482C23×C4—2921no—
483C23×C4—2921no—
484C23×C4—2921no—
485C23×C4—2921no—
486C23×C4—731no—
487C23×C4—731no—
488C23×C4—731no—
489C23×C4—731no—
490C23×C4—731no—
491C23×C4C22×D7311yescharacteristic
492C23×C4C22×D7311yescharacteristic
493C2×M16—2921no—
494C2×M16—2921no—
495C2×M16—2921no—
496C22×C8—731no—
497C22×C8—731no—
498C22×C8—731no—
499C22×C8—731no—
500C22×C8C22×D7311yescharacteristic
501C22×C8C22×D7311yescharacteristic
502C22×C8C22×D7311yescharacteristic
503C22×C8C22×D7311yescharacteristic
504#120—1464no—
505C4×D4—41no—
506C4×D4—41no—
507C4×D4—2921no—
508C4×D4—2921no—
509C4×D4—2921no—
510C4×D4—2921no—
511C2×C4⋊C4—731no—
512C2×C4⋊C4—731no—
513C2×C4⋊C4C4×D7311yescharacteristic
514C2×C22⋊C4—731no—
515C2×C22⋊C4—731no—
516C2×C22⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C22⋊C4—731no—
519C2×C22⋊C4—731no—
520C2×C22⋊C4—731no—
521C2×C22⋊C4—731no—
522C2×C22⋊C4—731no—
523C2×C22⋊C4—731no—
524C2×C22⋊C4C4×D7311yescharacteristic
525C2×C22⋊C4C4×D7311yescharacteristic
526C2×C42—731no—
527C2×C42—731no—
528C2×C42C22×D7311yescharacteristic
529C4⋊C8—41no—
530C4⋊C8—2921no—
531C4⋊C8—2921no—
532C22⋊C8—41no—
533C22⋊C8—41no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—2921no—
537C22⋊C8—2921no—
538C22⋊C8—2921no—
539C22⋊C8—2921no—
540C22⋊C8—2921no—
541C22⋊C8—2921no—
542C22⋊C8—2921no—
543C22⋊C8—2921no—
544C22⋊C8—2921no—
545C22⋊C8—2921no—
546C22⋊C8—2921no—
547#97—2921no—
548C4×C8—41no—
549C4×C8—2921no—
550#95—731no—
551#95—731no—
552#95—731no—
553#95—731no—
554#95—731no—
555#95—731no—
556C24—2921no—
557C24—2921no—
558C24—2921no—
559C24—2921no—
560C24—731no—
561C24—731no—
562C24—1462no—
563C24—1462no—
564C24—1462no—
565C24C2×C4×D7311yescharacteristic
566C24C2×C4×D7311yescharacteristic
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—41no—
570C2×D4—2921no—
571C2×D4—2921no—
572C2×D4—2921no—
573C2×D4—1462no—
574C2×D4—1462no—
575C2×D4—1462no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—2921no—
589C22×C4—2921no—
590C22×C4—2921no—
591C22×C4—2921no—
592C22×C4—2921no—
593C22×C4—2921no—
594C22×C4—2924no—
595C22×C4—2924no—
596C22×C4—2924no—
597C22×C4—2924no—
598C22×C4—2921no—
599C22×C4—2921no—
600C22×C4—2921no—
601C22×C4—731no—
602C22×C4—731no—
603C22×C4—731no—
604C22×C4—731no—
605C22×C4—731no—
606C22×C4—731no—
607C22×C4—1461no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4—1461no—
612C22×C4—1461no—
613C22×C4—1461no—
614C22×C4—1461no—
615C22×C4—1461no—
616C22×C4—1461no—
617C22×C4—1461no—
618C22×C4—1461no—
619C22×C4C2×C4×D7311yescharacteristic
620C22×C4C2×C4×D7311yescharacteristic
621C22×C4C2×C4×D7311yescharacteristic
622C22×C4C2×C4×D7311yescharacteristic
623C22×C4C23×D7311yescharacteristic
624M16—2924no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—1461no—
638C2×C8—1461no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8—1461no—
645C2×C8—1461no—
646C2×C8—1461no—
647C2×C8—1461no—
648C2×C8—1461no—
649C4⋊C4—41no—
650C4⋊C4—2921no—
651C4⋊C4—2921no—
652C22⋊C4—41no—
653C22⋊C4—41no—
654C22⋊C4—2921no—
655C22⋊C4—2921no—
656C22⋊C4—2921no—
657C22⋊C4—2921no—
658C22⋊C4—2921no—
659C22⋊C4—734no—
660C22⋊C4—1462no—
661C22⋊C4—1462no—
662C22⋊C4—1462no—
663C22⋊C4—1462no—
664C42—21no—
665C42—21no—
666C42—1461no—
667C42—1461no—
668C42—1461no—
669C42—1461no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—2924no—
684C23—2924no—
685C23—2924no—
686C23—2924no—
687C23—2924no—
688C23—2924no—
689C23—2924no—
690C23—732no—
691C23—732no—
692C23—1461no—
693C23—1461no—
694C23—1461no—
695C23—1461no—
696C23—1461no—
697C23—1461no—
698C23—1461no—
699C23—1461no—
700C23—1461no—
701C23—1461no—
702C23—1461no—
703C23—1461no—
704C23#1455659712yes—
705C23C22×C4×D7311yescharacteristic
706D4—44no—
707D4—2924no—
708D4—2924no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—2924no—
729C2×C4—2924no—
730C2×C4—2924no—
731C2×C4—2921no—
732C2×C4—2921no—
733C2×C4—2921no—
734C2×C4—2921no—
735C2×C4—2921no—
736C2×C4—2921no—
737C2×C4—2921no—
738C2×C4—2921no—
739C2×C4—732no—
740C2×C4—1461no—
741C2×C4—1461no—
742C2×C4—1461no—
743C2×C4—1461no—
744C2×C4—1461no—
745C2×C4—1461no—
746C2×C4—1461no—
747C2×C4—1461no—
748C2×C4—1461no—
749C2×C4—1461no—
750C2×C4—1461no—
751C2×C4—1461no—
752C2×C4—1461no—
753C2×C4—1461no—
754C2×C4—1461no—
755C2×C4—1461no—
756C2×C4—1461no—
757C2×C4M16×D7312yes—
758C2×C4#1455663611yescharacteristic
759C2×C4#1455663611yescharacteristic
760C2×C4#1455663611yescharacteristic
761C2×C4#1455663611yescharacteristic
762C2×C4#1455663711yescharacteristic
763C2×C4#1455663711yescharacteristic
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C8—2921no—
769C8—2921no—
770C8—2921no—
771C8—2921no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—29216no—
787C22—2921no—
788C22—2921no—
789C22—2921no—
790C22—2921no—
791C22—2921no—
792C22—2921no—
793C22—2921no—
794C22—2921no—
795C22—1462no—
796C22—1462no—
797C22—1462no—
798C22—1462no—
799C22—1462no—
800C22—1462no—
801C22#1798905911yescharacteristic
802C22#1798905911yescharacteristic
803C22#1798906011yescharacteristic
804C22C2×M16×D7311yescharacteristic
805C22#131×D7311yescharacteristic
806C22C2×#1455659711yescharacteristic
807C22#1798935211yescharacteristic
808C4—22no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—2921no—
813C4—2921no—
814C4—2921no—
815C4—2921no—
816C4—2921no—
817C4—1462no—
818C4#1798932411yescharacteristic
819C4#1798932511yescharacteristic
820C4#1798932511yescharacteristic
821C4#1798932911yescharacteristic
822C2—42no—
823C2—81no—
824C2—2922no—
825C2—2922no—
826C2#2261306811yescharacteristic
827C2#2261896211yescharacteristic
828C2#2261896311yescharacteristic
829C2#2261896911yescharacteristic
830C2#2261897311yescharacteristic
831C2#2261897411yescharacteristic
832C2#2261898411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1954C2
prime radicalC2×#14556559C4
cosocleC22×C4×C73C24
hypercenter#1954D73
hypocenterC73#23308
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1954

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22610727C2semidirect
3. #22610723C2semidirect
4. #22610543C2semidirect
5. #22610541C2semidirect
6. #22610537C2semidirect
7. #22610537C2semidirect
8. #22610536C2semidirect
9. #22610534C2semidirect
10. #22610229C2semidirect
11. #22610226C2semidirect
12. #22610226C2semidirect
13. #22609840C2semidirect
14. #22609840C2semidirect
15. C73×#1954C2semidirect
17. C22×#11924012C22semidirect
21. C2×#14556520C22semidirect
22. C2×#14556520C22semidirect
25. C2×C22⋊#10596831C22semidirect
34. C2×#14556501C22semidirect
35. C2×C8×Dic73C22semidirect
46. #17988342C22semidirect
47. #17988342C22semidirect
48. #17988341C22semidirect
49. #17988341C22semidirect
50. #17988341C22semidirect
51. #17988341C22semidirect
53. C2×C4⋊C8×C73C22semidirect
56. C2×C22⋊C8×C73C22semidirect
57. C2×C22⋊C8×C73C22semidirect
58. C2×C4×C8×C73C22semidirect
209. #11924005M16semidirect
420. #1954D73semidirect
432. C73#23308semidirect
441. C2×C4⋊C8C2×D73semidirect
455. C2×C22⋊C8C2×D73semidirect
456. C2×C22⋊C8C2×D73semidirect
459. C2×C4×C8C2×D73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#145565592
#226107272
#226107232
#226105432
#226105412
#226105372
#226105362
#226105342
#226102292
#226102262
#226098402
C73×#19542
#2330873